Game Engine object getting darker as it scales
What shading mode are you using? (Multitexture or GLSL) 

Multitexture

In this mode the the colors of the vertices are calculated from distance to the lamps. The pixels of the face are interpolated from colors of the vertices. As your vertices are more far away from the lamps they are rendered darker. The interpolation will be between dark colors and other dark colors. This method is fast but assumes that face pixels have no significant different distance to the lamps than vertices. 



In other words: It is assumed, objects closer to lamps have a denser mesh (smaller faces). This way the interpolation is not that much noticeable. 

Test: You will see a significant different effect when you subdivide the plane just once as the middle vertex is close to the lamps. 

GLSL

In this mode you should not see this effect as all pixels of the plane get the color dependent on the distance to the lamp (rather than interpolation).